x² /x + 1 dx -1 2.

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: Given: I=∫244x3x4-6x2+9dx For evaluating given integral, first we simplify it So,…

Q: use the graph of the function √²³ (x³²-6x) dx to explain the geometric meaning of the value of the…

A: Given function ∫03 (x3-6x) dx This below image is the graph of the function

Q: Find the indefinite integral and check the result by differentiation                   ∫x2(6 − x3)5…

A:

Q: Find the indefinite integral and check the result by differentiation.

A: We have to find indefinite integral and we have to check the result by differentiation: ∫sin x-6 cos…

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A:

Q: Evaluate the definite integral. (x* – 2x3 + 6x) dx

A: Given: ∫03x4-2x3+6xdx

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: Given: ∫01e-2xdx

Q: Find the indefinite integral and check the result by differentiation.

A: We have to calculate; I=∫5cosx + 4sinxdx

Q: 23. (x + 1)(3x – 2) dx

A:

Q: 17. x dx

A:

Q: Evaluate the definite integral. '(15 - 6x) dx

A:

Q: Find the indefinite integral and check the result by differentiation.

A:

Q: Evaluate the definite integral. (2x - 5) dx

A:

Q: Find the indefinite integral and check the result by differentiation.                     ∫(5 cos x…

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: The given definite integral is ∫182xdx. ∫182xdx=2xx-∫-12x12dx18=2xx-(-2x)18=2xx+2x18=8-22

Q: Evaluate the definite integral 2 x* +3x' -dx 1

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A:

Q: 4) S 2 sin x dx

A: We can find the integration and check it as below

Q: Find the indefinite integral and check the result by differentiation. ∫ 1/x5 dx

A:

Q: Find the indefinite integral and check the result by differentiation.

A: Given, I=∫x34+1dx Or  I=∫x34+1dx

Q: Find the indefinite integral and check the result by differentiation

A: Explanation: Given that, ∫x2(6-x3)5dx   Substitute the  u=6-x3du=-3x2dxdx=du-3x2   Now put this…

Q: Evaluate the definite integral. Use a graphing utility to verify your results. 49 dx /1

A:

Q: Find the indefinite integral and check the result by differentiation.

A: Given: I=∫dx2x We know that ∫xndx=xn+1n+1+c                                                   ..1

Q: Find the indefinite integral and check the result by differentiation. ∫3√x2 dx

A:

Q: Find the indefinite integral and check the result by differentiation.                   ∫(x3/2 + 2x…

A: Recall: Integral of xndx = xn+1 / (n + 1)  + C

Q: Find the indefinite integral and check the result by differentiation.

A: Consider the provided integral, ∫2-3x10dx Find the indefinite integral and check the result by…

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: Given: ∫01 x-x3dx To evaluate: The definite integral and using graphing to verify the answer.

Q: Find the indefinite integral and check the result by differentiation.

A:

Q: Evaluate the definite integral. x/2 -(sin x)13 dx dx

A: Given ∫0π/2ddx(sinx)13dx We have to evaluate the integral between 0 to π2

Q: Evaluate the definite integral. Use a graphing utility to verify your result

A: Given integral ∫45x2x-6dx Substitute  u=2x-6 Upper limit at x=5 is 2. Lower limit at x= is 2…

Q: Evaluate the definite integral

A: Given : ∫-212xdx

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: Definition used -            Definite integral -                         ∫abf(x)dx =F(b)-F(a)

Q: Find the indefinite integral and check the result by differentiation.

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: Given: ∫082xx2+36 dx

Q: Find the indefinite integral and check the result by differentiation                     ∫7x / (1 −…

A: ∫xndx=xn+1n+1+C

Q: Find the indefinite integral and check the result by differentiation                   ∫(x2 −…

A: Given, I=∫x2-932x dx

Q: Evaluate the definite integral

A: Evaluate definite integral.

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: It is given that  I=∫134x+1+2x dx=4∫134x dx+∫132x dx =4I1+I2…

Q: Find the indefinite integral and check the result by differentiation                     ∫x2 / (1 +…

A: Find the indefinite integral and check the result by differentiation                     ∫x2 / (1 +…

Q: Find the indefinite integral and check the result by differentiation                 ∫5x 3√(1 − x2)…

A: Given integral is ∫5x31-x2dx.

Q: Evaluate the definite integral two ways: first by a r-substitution in the definite integral and then…

A: The given integral,       ∫08x1+xdx

Q: 3 3 x cosx dx -3

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: we have the integral  ∫0453x+1dx we will use the formula  ∫1ax+bdx=1alog(ax+b)+c

Q: Find the indefinite integral and check the result by differentiation.              ∫(13 − x) dx

A:

Q: Find the indefinite integral and check the result by differentiation                    ∫x(5x2 + 4)3…

A: The given integral ∫x5x2+43dx can be evaluated as, ∫x5x2+43dx=∫x5x23+35x22×4+35x216+43dx…

Q: Evaluate the definite integral. Use a graphing utility to verify your result. (x³ + 1)² dx

A:

Q: Find the indefinite integral and check the result by differentiation                     ∫ x /√(1 −…

A: Given indefinite integral ∫x1-x2dx Substitute the value of 1-x2=t and differentiate it w.r.t "x"…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.